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<p><dfn class="terminology">Remark</dfn> Equation (<a href="" class="xref" data-knowl="./knowl/eq2_17.html" title="Equation 2.4.2">(2.4.2)</a>) is not the general solution since it does not include the solution <span class="process-math">\(y=0\text{,}\)</span> although it contains an arbitrary constant. Only for linear ODE, we use the terminology “general solution". You can also see other differences, such as the solution to the linear solution is explicit while the solution to the non-linear equation may be implicit.</p>
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